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Journal of Industrial and Management Optimization

March 2020 , Volume 16 , Issue 2

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Strong vector equilibrium problems with LSC approximate solution mappings
Nguyen Ba Minh and Pham Huu Sach
2020, 16(2): 511-529 doi: 10.3934/jimo.2018165 +[Abstract](3260) +[HTML](1138) +[PDF](419.84KB)

This paper introduces two classes of parametric strong vector equilibrium problems whose approximate solution mappings are lower semicontinuous. In the first class, the objective set-valued maps satisfy some cone-convexity/cone-concavity assumptions, and in the second one, they satisfy some strongly proper cone-quasiconvexconcavity assumptions. All these mentioned concepts of generalized cone-convexity/cone-concavity/ strongly proper cone-quasiconvexconcavity are new and different from the traditional ones. Some upper semicontinuity/continuity results are also obtained. Applications to parametric weak u-set and l-set optimization problems and weak vector multivalued equilibrium problems are given.

Continuous-time mean-variance portfolio selection with no-shorting constraints and regime-switching
Ping Chen and Haixiang Yao
2020, 16(2): 531-551 doi: 10.3934/jimo.2018166 +[Abstract](3810) +[HTML](1232) +[PDF](513.66KB)

The present article investigates a continuous-time mean-variance portfolio selection problem with regime-switching under the constraint of no-shorting. The literature along this line is essentially dominated by the Hamilton-Jacobi-Bellman (HJB) equation approach. However, in the presence of switching regimes, a system of HJB equations rather than a single equation need to be tackled concurrently, which might not be solvable in terms of classical solutions, or even not in the weaker viscosity sense as well. Instead, we first introduce a general result on the sign of geometric Brownian motion with jumps, then derive the efficient portfolio and frontier via the maximum principle approach; in particular, we observe, under a mild technical assumption on the initial conditions, that the no-shorting constraint will consistently be satisfied over the whole finite time horizon. Further numerical illustrations will be provided.

A two-warehouse probabilistic model with price discount on backorders under two levels of trade-credit policy
Sankar Kumar Roy, Magfura Pervin and Gerhard Wilhelm Weber
2020, 16(2): 553-578 doi: 10.3934/jimo.2018167 +[Abstract](4712) +[HTML](1317) +[PDF](731.96KB)

It is impossible in this competitive era to assess the demand for items in advance. So, it is essential to refer to a stochastic demand function. In this paper, a probabilistic inventory model for deteriorating items is unfolded. Here, the supplier as well as the retailer adopt the trade-credit policy for their customers with the aim of promoting the market competition. Shortages are included into the model, and when stock on hand is zero, the retailer offers a price discount to those customers who are willing to back-order their demands. We consider two different warehouses in which the first one is an Own Warehouse (OW) where the deterioration is constant over time and the other is a Rented Warehouse (RW), and where the deterioration rate follows a Weibull distribution. An algorithm is provided for finding the solutions of the formulated model.Global convexity of the cost function is established which shows that our proposed model is very helpful for any supplier or retailer to finalize the optimal ordering policy. Beside of this, we target to increase the total profit for retailer by reducing the corresponding total inventory cost. The theoretical concept is justified with the help of some numerical examples. A sensitivity analysis of the optimal solution with respect to the major parameters is also provided in order to stabilize our model. We finalize the paper through a conclusion and a preview onto possible future studies.

Identification and robustness analysis of nonlinear hybrid dynamical system of genetic regulation in continuous culture
Qi Yang, Lei Wang, Enmin Feng, Hongchao Yin and Zhilong Xiu
2020, 16(2): 579-599 doi: 10.3934/jimo.2018168 +[Abstract](3044) +[HTML](1226) +[PDF](1045.19KB)

In this paper, we present a framework to infer the possible transmembrane transport of intracellular substances. Considering four key enzymes, a modified fourteen-dimensional nonlinear hybrid dynamic system is established to describe the microbial continuous culture with enzyme-catalytic and genetic regulation. A novel quantitative definition of biological robustness is proposed to characterize the system's resilience when system parameters were perturbed. It not only considers the expectation of system output data after parameter disturbance but also considers the influence of the variance of these data. In this way, the definition can be used as an objective function of the system identification model due to the lack of data on the concentration of intracellular substances. Then, we design a parallel computing method to solve the system identification model. Numerical results indicate that the most likely transmembrane mode of transport is active transport coupling with passive diffusion for glycerol and 1, 3-propanediol.

Evaluation strategy and mass balance for making decision about the amount of aluminum fluoride addition based on superheat degree
Weichao Yue, Weihua Gui, Xiaofang Chen, Zhaohui Zeng and Yongfang Xie
2020, 16(2): 601-622 doi: 10.3934/jimo.2018169 +[Abstract](3638) +[HTML](1252) +[PDF](2017.44KB)

The purpose of aluminum fluoride (AlF3) addition is to adjust the superheat degree (SD) in the aluminum reduction process. Determining the appropriate amount of AlF3 to add has long been a challenging industrial issue as a result of its inherent complexity. Because of the decreasing number of experienced technicians, the manual addition of AlF3 is usually inexact, which easily leads to an unstable cell condition. In this paper, an evaluation strategy based on the SD for AlF3 addition is proposed. An extended naïve Bayesian classifier (ENBC) is designed to estimate the states of SD and its trends that represent the current and potential cell condition respectively, and then the process is graded by evaluating the estimated results based on fuzzy theory. The reduction process is divided into a few situations based on the evaluation grades, and mass balance is introduced to determine the amount of AlF3 addition in each situation. The results of experiments show that the proposed strategy is feasible, and the effectiveness of AlF3 addition is improved compared to the existing method. Moreover, automatic AlF3 addition is promising based on the proposed strategy.

Optimality conditions for multiobjective fractional programming, via convexificators
Mansoureh Alavi Hejazi and Soghra Nobakhtian
2020, 16(2): 623-631 doi: 10.3934/jimo.2018170 +[Abstract](3805) +[HTML](1304) +[PDF](348.28KB)

In this paper, the idea of convexificators is used to derive the Karush-Kuhn-Tucker necessary optimality conditions for local weak efficient solutions of multiobjective fractional problems involving inequality and equality constraints. In this regard, several well known constraint qualifications are generalized and relationships between them are investigated. Moreover, some examples are provided to clarify our results.

A new method for ranking decision making units using common set of weights: A developed criterion
Gholam Hassan Shirdel and Somayeh Ramezani-Tarkhorani
2020, 16(2): 633-651 doi: 10.3934/jimo.2018171 +[Abstract](3697) +[HTML](1316) +[PDF](407.7KB)

In this paper we have developed a new model by altering Liu and Peng's approach [20] toward ranking method using CSW. In fact, we have adopted a new criterion which is stronger in terms of maximizing efficiencies. After showing advantages of our model theoretically and illustrating it geometrically, two examples demonstrated how the proposed method is practically more capable.

Designing a hub location and pricing network in a competitive environment
Maryam Esmaeili and Samane Sedehzade
2020, 16(2): 653-667 doi: 10.3934/jimo.2018172 +[Abstract](6409) +[HTML](1444) +[PDF](547.42KB)

This paper models a novel mixed hub location and pricing problem in a network consists of two competitive firms with different economic positions (Stackelberg-game). The flow that reflects demand of each firm directly depends on its price (Bernard's model). The flow of each firm directly depends on both firms' prices simultaneously (Bernard's model). The firm with higher position (the leader) chooses its potential hubs while the firm in lower position (the follower) may choose either its own hub locations or the other firm's existing hub locations (the competitor's hub) through two real contracts; the airlines own and the long term usage contracts. Firms have to make decision on both the location-allocation and the price determination problems through maximizing their own profits. Moreover, firms make decisions for extending hub coverage through establishing new airline bands, gates and other infrastructures by considering extra cost. In order to evaluate the proposed model, an example derived from the CAB dataset has been solved using Imperialist Competitive Algorithm (ICA) and closed expression, respectively for the hub location-allocation and pricing decisions. Finally, a sensitivity analysis of the model is conducted to show the effect of each firm's share of fixed costs on the contract type selection.

Shipper collaboration in forward and reverse logistics
Xiaohui Lyu, Nengmin Wang, Zhen Yang and Haoxun Chen
2020, 16(2): 669-705 doi: 10.3934/jimo.2018173 +[Abstract](5336) +[HTML](1340) +[PDF](849.08KB)

In less than truckload transportation, shippers collaborate to reduce their logistics costs by consolidating their transportation requests in the procurement of transportation services from a carrier for serving the requests. In this paper, we study shipper collaboration in forward and reverse logistics, in which multiple shippers with forward or/and reverse logistics operations consolidate their transportation requests. In the forward and reverse logistics, manufacturers deliver new products to their customers and used products are collected from customers and transported to remanufacturers for repair or reproduction. This gives rise to a new vehicle routing problem with pickup and delivery requests and three different types of depots (product depots, vehicle depots and recycle depots). A hybrid approach combining greedy randomized adaptive search procedure (GRASP) and iterated local search (ILS) is proposed to find a near optimal solution of the problem. Numerical experiments on a large set of randomly generated instances with different problem sizes demonstrate that shipper collaboration in forward and reverse logistics can realize significant cost savings compared with the isolated operation of each shipper without cooperation, and the proposed approach is effective in the sense that it can find a high quality solution in a reasonable computation time.

Vector-valued separation functions and constrained vector optimization problems: optimality and saddle points
Jiawei Chen, Shengjie Li and Jen-Chih Yao
2020, 16(2): 707-724 doi: 10.3934/jimo.2018174 +[Abstract](3438) +[HTML](1040) +[PDF](438.64KB)

In this paper, we consider a class of constrained vector optimization problems by using image space analysis. A class of vector-valued separation functions and a \begin{document}$ \mathfrak{C} $\end{document}-solution notion are proposed for the constrained vector optimization problems, respectively. Moreover, existence of a saddle point for the vector-valued separation function is characterized by the (regular) separation of two suitable subsets of the image space. By employing the separation function, we introduce a class of generalized vector-valued Lagrangian functions without involving any elements of the feasible set of constrained vector optimization problems. The relationships between the type-Ⅰ(Ⅱ) saddle points of the generalized Lagrangian functions and that of the function corresponding to the separation function are also established. Finally, optimality conditions for \begin{document}$ \mathfrak{C} $\end{document}-solutions of constrained vector optimization problems are derived by the saddle-point conditions.

Optimal pricing and inventory strategies for introducing a new product based on demand substitution effects
Zhijie Sasha Dong, Wei Chen, Qing Zhao and Jingquan Li
2020, 16(2): 725-739 doi: 10.3934/jimo.2018175 +[Abstract](3272) +[HTML](1316) +[PDF](389.25KB)

This paper studies a single-period inventory-pricing problem with two substitutable products, which is very important in the area of Operations Management but has received little attention. The proposed problem focuses on determining the optimal price of the existing product and the inventory level of the new product. Inspired by practice, the problem considers various pricing strategies for the existing product as well as the cross elasticity of demand between existing and new products. A mathematical model has been developed for different pricing strategies to maximize the expected profit. It has been proven that the objective function is concave and there exists the unique optimal solution. Different sets of computational examples are conducted to show that the optimal pricing and inventory strategy generated by the model can increase profits.

Risk-balanced territory design optimization for a Micro finance institution
Jesús Fabián López Pérez, Tahir Ekin, Jesus A. Jimenez and Francis A. Méndez Mediavilla
2020, 16(2): 741-758 doi: 10.3934/jimo.2018176 +[Abstract](3070) +[HTML](1057) +[PDF](535.66KB)

Micro finance institutions (MFIs) play an important role in emerging economies as part of programs that aim to reduce income inequality and poverty. A territory design that balances the risk of branches is important for the profitability and long-term sustainability of a MFI. In order to address such particular business needs, this paper proposes a novel risk-balanced territory planning model for a MFI. The proposed mixed integer programming model lets the MFI choose the location of the branches to be designated as territory centers and allocate the customers to these centers with respect to planning criteria such as the total workload, monetary amount of loans and profit allocation while balancing the territory risk. This model is solved using a branch and cut based hybrid-heuristic framework. We discuss the impact of the risk balancing and merits of the proposed model.

Multi-objective robust cross-market mixed portfolio optimization under hierarchical risk integration
Han Yang, Jia Yue and Nan-jing Huang
2020, 16(2): 759-775 doi: 10.3934/jimo.2018177 +[Abstract](3286) +[HTML](1121) +[PDF](642.4KB)

In this paper, we consider a multi-objective robust cross-market mixed portfolio optimization model under hierarchical risk integration in the international financial market consisting of finite sub-markets. It is difficult to describe the dependent structure accurately by the traditional copula theory because of the dependent structures of the risk assets in finite sub-markets are different usually. By employing the hierarchical risk integration method, we establish the multi-objective robust cross-market mixed portfolio model in which the worst-case value at risk is used as the risk measurement and the transaction costs, skewness and investment proportion limitation are all considered. We provide a new algorithm to calculate the worst-case value at risk of the cross-market mixed portfolio and give a numerical experiment to show the superiority of the model considered in this paper.

A real-time pricing scheme considering load uncertainty and price competition in smart grid market
Yeming Dai, Yan Gao, Hongwei Gao, Hongbo Zhu and Lu Li
2020, 16(2): 777-793 doi: 10.3934/jimo.2018178 +[Abstract](3669) +[HTML](1178) +[PDF](447.19KB)

As a powerful tool of Demand Response (DR) techniques in smart grid market, Real-time Pricing (RTP) may optimize the electricity consumption pattern of users and improve the efficiency of electricity market. In this paper, a multi-leader-follower Stackelberg Game (SG) based on RTP is established to model the strategic interaction behavior between multiple electricity retailers and multiple users while simultaneously considering the power load uncertainty of users and the price competition among electricity retailers. In the game model, electricity retailers aim to seek their revenue maximization while the optimal power consumption competition among the users is taken into account. Lagrange multiplier method is utilized to solve the Nash Equilibriums (NE) of two non-cooperative games, and the closed-form optimal solution is obtained, then the Stackelberg Equilibrium (SE) consisting of the optimal real-time prices of electricity retailers and the power consumption of users is given. Finally, the numerical analysis results verify that the proposed scheme can reduce the real-time electricity price and increase the users' satisfaction under feasible constraint, which shows the effectiveness and better performance of proposed RTP scheme.

An executive model for network-level pavement maintenance and rehabilitation planning based on linear integer programming
Mahmoud Ameri and Armin Jarrahi
2020, 16(2): 795-811 doi: 10.3934/jimo.2018179 +[Abstract](3645) +[HTML](1171) +[PDF](788.83KB)

Although having too many details can complicate the planning process, this study involves the formulating of an executive model having a broad range of parameters aimed at network-level pavement maintenance and rehabilitation planning. Four decomposed indicators are used to evaluate the pavement conditions and eight maintenance and rehabilitation categories are defined using these pavement quality indicators. As such, some restrictions called ''technical constraints" are defined to reduce complexity of solving procedure. Using the condition indicators in the form of normalized values and developing technical constraints in a linear integer programming model has improved network level pavement M&R planning. The effectiveness of the developed model was compared by testing it under with-and-without technical constraints conditions over a 3-year planning period in a 10-section road network. It was found that using technical constraints reduced the runtime in resolving the problem by 91%, changed the work plan by 13%, and resulted in a cost increase of 1.2%. Solving runtime reduction issues can be worthwhile in huge networks or long-term planning durations.

Continuous-time mean-variance asset-liability management with stochastic interest rates and inflation risks
Huai-Nian Zhu, Cheng-Ke Zhang and Zhuo Jin
2020, 16(2): 813-834 doi: 10.3934/jimo.2018180 +[Abstract](6472) +[HTML](1183) +[PDF](597.76KB)

This paper investigates a continuous-time Markowitz mean-variance asset-liability management (ALM) problem under stochastic interest rates and inflation risks. We assume that the company can invest in $n + 1$ assets: one risk-free bond and $n$ risky stocks. The risky stock's price is governed by a geometric Brownian motion (GBM), and the uncontrollable liability follows a Brownian motion with drift, respectively. The correlation between the risky assets and the liability is considered. The objective is to minimize the risk (measured by variance) of the terminal wealth subject to a given expected terminal wealth level. By applying the Lagrange multiplier method and stochastic control approach, we derive the associated Hamilton-Jacobi-Bellman (HJB) equation, which can be converted into six partial differential equations (PDEs). The closed-form solutions for these six PDEs are derived by using the homogenization approach and the variable transformation technique. Then the closed-form expressions for the efficient strategy and efficient frontier are obtained. In addition, a numerical example is presented to illustrate the results.

Generalized ADMM with optimal indefinite proximal term for linearly constrained convex optimization
Fan Jiang, Zhongming Wu and Xingju Cai
2020, 16(2): 835-856 doi: 10.3934/jimo.2018181 +[Abstract](3687) +[HTML](994) +[PDF](543.76KB)

We consider the generalized alternating direction method of multipliers (ADMM) for linearly constrained convex optimization. Many problems derived from practical applications have showed that usually one of the subproblems in the generalized ADMM is hard to solve, thus a special proximal term is added. In the literature, the proximal term can be indefinite which plays a vital role in accelerating numerical performance. In this paper, we are devoted to deriving the optimal lower bound of the proximal parameter and result in the generalized ADMM with optimal indefinite proximal term. The global convergence and the \begin{document}$ O(1/t) $\end{document} convergence rate measured by the iteration complexity of the proposed method are proved. Moreover, some preliminary numerical experiments on LASSO and total variation-based denoising problems are presented to demonstrate the efficiency of the proposed method and the advantage of the optimal lower bound.

An iterated greedy algorithm with variable neighborhood descent for the planning of specialized diagnostic services in a segmented healthcare system
Rodolfo Mendoza-Gómez, Roger Z. Ríos-Mercado and Karla B. Valenzuela-Ocaña
2020, 16(2): 857-885 doi: 10.3934/jimo.2018182 +[Abstract](3124) +[HTML](1161) +[PDF](697.21KB)

In this paper, a problem arising in the planning of specialized diagnostic services in a segmented public healthcare system is addressed. The problem consists of deciding which hospitals will provide the service and their capacity levels, the allocation of demand in each institution, and the reallocation of uncovered demand to other institutions or private providers, while minimizing the total equivalent annual cost of investment and operating cost required to satisfy all the demand. An associated mixed-integer linear programming model can be solved by conventional branch and bound for relatively small instances; however, for larger instances the problem becomes intractable. To effectively address larger instances, a hybrid metaheuristic framework combining iterated greedy (IGA) and variable neighborhood descent (VND) components for this problem is proposed. Two greedy construction heuristics are developed, one starting with an infeasible solution and iteratively adding capacity and the other starting with a feasible, but expensive, solution and iteratively decrease capacity. The iterated greedy algorithm includes destruction and reconstruction procedures. Four different neighborhood structures are designed and tested within a VND procedure. In addition, the computation of local search components benefit from an intelligent exploitation of problem structure since, when the first-level location variables (hospital location and capacity) are fixed, the remaining subproblem can be solved efficiently as it is very close to a transshipment problem. All components and different strategies were empirically assessed both individually and within the IGA-VND framework. The resulting metaheuristic is able to obtain near optimal solutions, within 3% of optimality, when tested over a data base of 60- to 300-hospital instances.

Financing strategies for a capital-constrained supplier under yield uncertainty
Hongjun Peng and Tao Pang
2020, 16(2): 887-909 doi: 10.3934/jimo.2018183 +[Abstract](3987) +[HTML](1086) +[PDF](795.13KB)

We consider a supply chain consisting of a supplier and a distributor, in which the supplier has a capital constraint and faces productivity yield uncertainty. To solve the capital constraint problem, we propose an advance payment with risk compensation (APRC) mechanism, under which the distributor finances the supplier with an advance payment, and the supplier provides a price discount to compensate the distributor for the supplier's bankruptcy risk. The optimal solutions are derived under the APRC mechanism and the results indicate that under the APRC, the whole supply chain performs as well as if there is no capital constraint, in terms of profits and optimal strategies. Therefore, the APRC is an efficient solution for the supplier's capital constraint issue. In addition, when the deficit is big, the APRC provides an alternative financing arrangement and it can bring higher profits for both parties. Another very interesting finding is that, when the capital deficit is small, the supplier can do better with the bank loan financing, despite that a higher interest rate needs to be paid in this case.

Upper bounds for Z$ _1 $-eigenvalues of generalized Hilbert tensors
Juan Meng and Yisheng Song
2020, 16(2): 911-918 doi: 10.3934/jimo.2018184 +[Abstract](2614) +[HTML](912) +[PDF](330.26KB)

The Z\begin{document}$ _1 $\end{document}-eigenvalue of tensors (hypermatrices) was widely used to discuss the properties of higher order Markov chains and transition probability tensors. In this paper, we extend the concept of Z\begin{document}$ _1 $\end{document}-eigenvalue from finite-dimensional tensors to infinite-dimensional tensors, and discuss the upper bound of such eigenvalues for infinite-dimensional generalized Hilbert tensors. Furthermore, an upper bound of Z\begin{document}$ _1 $\end{document}-eigenvalue for finite-dimensional generalized Hilbert tensor is obtained also.

Extension of generalized solidarity values to interval-valued cooperative games
Deng-Feng Li, Yin-Fang Ye and Wei Fei
2020, 16(2): 919-931 doi: 10.3934/jimo.2018185 +[Abstract](3060) +[HTML](988) +[PDF](366.55KB)

The main purpose of this paper is to extend the concept of generalized solidarity values to interval-valued cooperative games and hereby develop a simplified and fast approach for solving a subclass of interval-valued cooperative games. In this paper, we find some weaker coalition monotonicity-like conditions so that the generalized solidarity values of the \begin{document}$ \alpha $\end{document}-cooperative games associated with interval-valued cooperative games are always monotonic and non-decreasing functions of any parameter \begin{document}$ \alpha \in [0,1] $\end{document}. Thereby the interval-valued generalized solidarity values can be directly and explicitly obtained by computing their lower and upper bounds through only using the lower and upper bounds of the interval-valued coalitions' values, respectively. The developed method does not use the interval subtraction and hereby can effectively avoid the issues resulted from it. Furthermore, we discuss the effect of the parameter \begin{document}$ \xi $\end{document} on the interval-valued generalized solidarity values of interval-valued cooperative games and some significant properties of interval-valued generalized solidarity values.

A new class of positive semi-definite tensors
Yi Xu, Jinjie Liu and Liqun Qi
2020, 16(2): 933-943 doi: 10.3934/jimo.2018186 +[Abstract](3083) +[HTML](980) +[PDF](342.54KB)

In this paper, a new class of positive semi-definite tensors, the MO tensor, is introduced. It is inspired by the structure of Moler matrix, a class of test matrices. Then we focus on two special cases in the MO-tensors: Sup-MO tensor and essential MO tensor. They are proved to be positive definite tensors. Especially, the smallest H-eigenvalue of a Sup-MO tensor is positive and tends to zero as the dimension tends to infinity, and an essential MO tensor is also a completely positive tensor.

Convergence analysis of a new iterative algorithm for solving split variational inclusion problems
Yan Tang
2020, 16(2): 945-964 doi: 10.3934/jimo.2018187 +[Abstract](3037) +[HTML](1269) +[PDF](291.75KB)

The split variational inclusion problem (SVIP) has been extensively studied and applied in real-world problems such as intensity-modulated radiation therapy (IMRT) and in sensor networks and in computerized tomography and data compression. Inspired by the works of L$\acute{o}$pez et al.$[24]$, Byrne et al.[10] and Sitthithakerngkiet et al.[34], as well as of Moudafi and Thukur[29], we propose a self-adaptive step size algorithm for solving split variational inclusion problem (SVIP) without the prior knowledge of the operator norms. Under more mild conditions we obtain weak convergence of the proposed algorithm. We also construct a self-adaptive step size two-step iterative algorithm which converges strongly to the minimum-norm element of the solution of the SVIP. Finally, the performances and computational examples are presented and a comparison with related algorithms is provided to illustrate the efficiency and applicability of our new algorithms.

An optimal maintenance strategy for multi-state systems based on a system linear integral equation and dynamic programming
Haibo Jin, Long Hai and Xiaoliang Tang
2020, 16(2): 965-990 doi: 10.3934/jimo.2018188 +[Abstract](3712) +[HTML](1127) +[PDF](2277.3KB)

An optimal preventive maintenance strategy for multi-state systems based on an integral equation and dynamic programming is described herein. Unlike traditional preventive maintenance strategies, this maintenance strategy is formulated using an integral equation, which can capture the system dynamics and avoid the curse of dimensionality arising from complex semi-Markov processes. The linear integral equation of the system is constructed based on the system kernel. A numerical technique is applied to solve this integral equation and obtain all of the mean elapsed times from each reliable state to each unreliable state. An analytical approach to the optimal preventive maintenance strategy is proposed that maximizes the expected operational time of the system subject to the total maintenance budget based on dynamic programming in which both backward and forward search techniques are used to search for the local optimal solution. Finally, numerical examples concerning two different scales of systems are presented to demonstrate the performance of the strategy in terms of accuracy and efficiency. Moreover a sensitivity analysis is provided to evaluate the robustness of the proposed strategy.

A symmetric Gauss-Seidel based method for a class of multi-period mean-variance portfolio selection problems
Ning Zhang
2020, 16(2): 991-1008 doi: 10.3934/jimo.2018189 +[Abstract](3339) +[HTML](1171) +[PDF](667.45KB)

It is commonly accepted that the estimation error of asset returns' sample mean is much larger than that of sample covariance. In order to hedge the risk raised by the estimation error of the sample mean, we propose a sparse and robust multi-period mean-variance portfolio selection model and show how this proposed model can be equivalently reformulated as a multi-block nonsmooth convex optimization problem. In order to get an optimal strategy, a symmetric Gauss-Seidel based method is implemented. Moreover, we show that the algorithm is globally linearly convergent. The effectiveness of our portfolio selection model and the efficiency of its solution method are demonstrated by empirical experiments on both the synthetic and real datasets.

A primal-dual interior-point method capable of rapidly detecting infeasibility for nonlinear programs
Yu-Hong Dai, Xin-Wei Liu and Jie Sun
2020, 16(2): 1009-1035 doi: 10.3934/jimo.2018190 +[Abstract](3546) +[HTML](1074) +[PDF](614.72KB)

With the help of a logarithmic barrier augmented Lagrangian function, we can obtain closed-form solutions of slack variables of logarithmic-barrier problems of nonlinear programs. As a result, a two-parameter primal-dual nonlinear system is proposed, which corresponds to the Karush-Kuhn-Tucker point and the infeasible stationary point of nonlinear programs, respectively, as one of two parameters vanishes. Based on this distinctive system, we present a primal-dual interior-point method capable of rapidly detecting infeasibility of nonlinear programs. The method generates interior-point iterates without truncation of the step. It is proved that our method converges to a Karush-Kuhn-Tucker point of the original problem as the barrier parameter tends to zero. Otherwise, the scaling parameter tends to zero, and the method converges to either an infeasible stationary point or a singular stationary point of the original problem. Moreover, our method has the capability to rapidly detect the infeasibility of the problem. Under suitable conditions, the method can be superlinearly or quadratically convergent to the Karush-Kuhn-Tucker point if the original problem is feasible, and it can be superlinearly or quadratically convergent to the infeasible stationary point when the problem is infeasible. Preliminary numerical results show that the method is efficient in solving some simple but hard problems, where the superlinear convergence to an infeasible stationary point is demonstrated when we solve two infeasible problems in the literature.

2021 Impact Factor: 1.411
5 Year Impact Factor: 1.441
2021 CiteScore: 2.1




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